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In 1981/82, Hickin \& Plotkin and McKenzie both proved that a finite grouphas only countably many non-isomorphic subdirect powers if and only if it isabelian. In this paper, we prove that a finite commutative semigroup has onlycountably many non-isomorphic countable subdirect powers if and only if it iseither a finite abelian group or a null semigroup.

On the number of countable subdirect powers of finite commutative semigroups